Energy device analysis and evaluation

ABSTRACT

A method and apparatus for creating, measuring and analyzing polarization voltages developed across an element, such as an electronic component or an electrochemical energy cell, or network of such elements, in response to a current mode excitation provided by a driver composed of a voltage controlled voltage source connected to one terminal of a Device Under Test and a voltage controlled current source connected to the other terminal of a Device Under Test. A voltage sensor, also connected across the Device Under Test, determines the magnitude and polarity of any potential appearing across the DUT; whenever the excitation current is exactly zero, this measured potential will be equal to the Open Circuit Potential of the DUT. This configuration of driver and sensor is known as a Kelvin connection. In response to the sensor&#39;s output, an internal control circuit adjusts the magnitude and polarity of an offset controlling signal provided to the voltage controlled voltage source, such that any intrinsic open circuit potential exhibited by the device under test appears centered with respect to the common ground potential of the apparatus. The offset controlling signal is also applied to the inputs of the sensor preamplifier such that the only the polarization voltage component of the DUT&#39;s voltage response to the excitation current appears at the output of the preamplifier. The characteristics of the resulting polarization voltage signal appearing at the output of the sensor preamplifier may be analyzed to yield both qualitative and quantitative information about the Device Under Test.

This application claims benefit of provisional application No.60/014,159 filed Mar. 27, 1996.

BACKGROUND OF THE INVENTION

The invention relates to energy device testing and evaluation.

A widely used technique for investigating the behavior of energy devicessuch as electrochemical cells or batteries is electrochemical impedancespectroscopy, also commonly known as frequency response analysis. SeeMacDonald, “Impedance Spectroscopy”, Wiley 1987. In general, thetechnique employs sinusoidal electric stimulation (AC voltage or currentof known amplitude, frequency, and phase) of a device under test.Measuring the resultant in-phase and quadrature components of thedevice's response allows calculation of the real and imaginarycomponents of the device impedance using Ohm's law (E=I*R or R=E/I). Bytaking a series of measurements over a range of frequencies, thecharacteristic response of the device under test is obtained. From theimpedance parameters, other quantities, such as, for example, phaseangle and modulus, may be derived.

Quantitative analysis is regularly achieved by using nonlinear leastsquares fitting to adjust parameters of a proposed theoretical model orelectronic circuit analog. A well chosen model will correspond to theunderlying chemical and kinetic processes. Frequency response analysisis very robust, but requires performance of multiple individual tests toobtain a complete frequency response profile. As such, the duration ofthe test process, especially if high resolution, low frequency responseinformation is required, may be considerable. In addition, the timedomain response of the device under test must be derived from apostulated equivalent circuit model, which means that accuracy of thederived response is strongly dependent on the validity of the model andthe accuracy of the raw data.

To overcome these concerns, a number of direct time domain measurementtechniques have been proposed. Commonly used techniques includevoltammetry, polarography, chronoamperometry and chronopotentiometry,among others. The distinguishing characteristic of these time domainmethods is that, instead of using a continuous sinusoid as theexcitation signal, they use continuous (usually linear or exponentiallyshaped) segments separated by discontinuities. Typical stimuli include,for example: triangle or square waves; a rectangular pulse or pulsetrain followed by return to a pre-stimulus condition; a composite signalsuch as a stepped potential staircase with a smaller signal superimposedon each step; or, finally, a series of alternating charge/dischargeevents.

For general laboratory applications where theoretical analysis ofreaction mechanisms is desired, time domain data may be analyzed usingwell known mathematical techniques, such as Fourier and Laplace integraltransforms. The Fourier method allows derivation of a cell's frequencyresponse, while the Laplace method yields impedance and admittanceinformation. When specifically applied to electrochemical accumulators(energy storage cells and batteries), time domain techniques may be usedto assess cell condition and infer a relative state of charge.

SUMMARY

The invention provides a highly accurate technique for measuring andanalyzing electric potential changes occurring in a device such as anelectric or electrochemical cell as a result of stimulation with asquare wave current. An electric cell here is distinguished from anelectrochemical cell in that voltage potential changes occurring in theelectric cell are indicative primarily of charge storage and energy losseffects due to dielectric behavior (e.g., lossy capacitor), whereaspotential changes observed in an electrochemical cell reflect additionalprocesses including physical changes (mass transport, diffusion) andvarious Faradaic electrochemical reactions.

The technique uses a progressive change of the polarization voltageacross a device, which develops over time in response to galvanicstimulation, as an estimator of device condition. Furthermore, suitablequantitative analyses of such changes in polarization, expressed as ajoint function of stimulation magnitude, polarity and duration, allowquantitative characterization of various underlying chemical processes,identification of anomalous (fault) conditions, and estimation of stateof charge.

The technique may be used to electronically measure devices that exhibitreversible or quasi-reversible reactions in response to a sufficientlysmall excitation signal symmetrically applied about the instantaneousequilibrium potential. While not all electrochemical systems have thisproperty, a significant number of commercial applications require theprecise measurement and characterization of just such devices. Thetechnique can be used to evaluate the time domain response of any systemwhich exhibits the property of electrical impedance.

The invention promises to help meet an ever growing need for reliableelectrochemical devices that can deliver electricity on demand, and inmany cases, be quickly and easily recharged for further use. Suchdevices include fuel cells, primary (single use) cells and batteries,and secondary (rechargeable) cells and batteries. There is acommensurate need for a technique for rapidly evaluating the state ofcharge and overall condition of such a device, regardless of whether thedevice is static (disconnected) or dynamically operating(charging/discharging).

The ability to rapidly perform a quantitative test of device conditionis particularly important when the device is being used to supply powerto a critical load, so that an unexpected failure may have seriousconsequences. Similarly, qualification testing during and immediatelyafter batteries or other electrochemical cells are produced, the chargeprocess would bring new economies to battery manufacturing. The sametechnique may be used in the field to perform tests prior to and aftersale. Finally, the technique may be used in the laboratory to provideimmediate information on electrochemical cell behavior under controlledconditions to support evolving battery technologies.

Polarization voltage is operationally defined in this document as thedifference between the cell potential just prior to the onset of astep-wise change in current stimulation (i.e., the leading edge of apulse or square wave) and the value attained at some specific later timeduring the stimulation. By employing high speed synchronous samplingmethods, the actual waveform of the polarization voltage that developsduring each half-period of the square wave excitation may be recordedfor later analysis.

Specifically, a bipolar square wave current exhibiting a 50% duty cycle(mark-space ratio=1) and an average DC current component of exactly zerois used to stimulate an electrochemical cell or accumulator. Theresultant polarization voltage response developed across the cell isrepetitively sampled at a plurality of points at corresponding positionsduring each of the repetitions of the waveform. Piecewise numericalintegration is performed by generating the sum of corresponding samplepoints from consecutive positive half cycles, and the separately the sumfor the negative half cycles, respectively. These sums are then eachdivided by the number of samples (N) yielding an average valueexhibiting a “Square Root of N” noise reduction factor. The relativeshape and size of these averaged curves may be then analyzed ortransformed as required to yield detailed information about thecondition and future performance of the electrochemical cell (orbattery). Data may be converted to digital format, using either a linearor exponentially spaced sampling algorithms. Linearly sampled data issuitable for processing with integral Laplace and Fourier transforms,while exponentially sampled data is useful for immediate graphicalpresentation of test results.

For chemical systems embodying reversible or quasireversible redoxreactions, it has been determined that, when the galvanic stimulationtakes the particular form of an even numbered sequence of square pulsesof alternating polarity and of sufficiently small amplitude to ensurethat cell response will be linear, the net charge transferred to thecell will be precisely zero. In addition, the resultant polarizationvoltage response will exhibit a characteristic symmetry about the timeaxis. Such a technique is, by definition, non-invasive. Any loss ofsymmetry detected in the polarization response is necessarily indicativeof a breach of one of the three initial conditions, and thus may serveas an indicator thereof.

When this technique is used to test batteries, immediate assessment ofcondition and relative state of charge can be made by plottingdeviations from the mean values. Mean value data is obtained frommeasurements of many known-good cells of the particular type. Thedeviations from these mean values obtained for the cell under test arethen calculated to produce a fingerprint that can be interpretedvisually for qualitative understanding.

Laplace transform techniques can be applied to calculated impedanceparameters to construct models of time domain behavior for individualunderlying processes, while the Fourier transform (and particularly theDFT) permits translation of the data into the frequency domain.

The technique facilitates rapid acquisition and analysis of energy cellstate of charge and overall condition. The technique permits ease of useand efficient, portable operation. The technique also facilitatesanalysis of cell state of charge and condition. An apparatus accordingto the technique may include a self centering and polarizing circuitwith respect to connection of test leads to a device under test thatexhibits an intrinsic bias potential. To this end, the circuitry mayinclude four connectors that include test leads each supplied withsuitable connecting clamps, clips or fixturing. The connectors areaffixed to terminals of the device under test, so that the connectionfor the non-inverting preamplifier input and the current drive signalare made to the same terminal of the device under test, while theconnections for the inverting preamplifier input and the current receivesignal are made to the opposite terminal of the device under test. Thisconnection method is known as a Kelvin connection.

The technique may provide a symmetric current signal to a cell undertest to produce a non-invasive test method. The technique may measureand report the voltage response of the cell under test to determinestate of charge and cell condition, and may process the voltage responseof a cell under test to remove from that signal a time invariantcomponent to isolate a time variant component.

The technique may be used with different types of energy devices. Forexample, detection of asymmetry between positive and negative half-cycleresponses may indicate a nonlinear transfer function, indicative, forexample, of semiconductor diode behavior within an electrode,characterizing severe discharge in lead acid cells. Similarly, therelative age of lithium ion cells (number of charge/discharge cyclesexperienced) can be estimated from relative separation of polarizationcurves when calls are otherwise equated for open circuit voltage.

A time variant component of the voltage response of a cell under testmay be sampled at periodic intervals to produce a linear representationof the signal. A time variant component of the voltage response of acell under test may be sampled at logarithmic intervals to produce alogarithmic representation of the signal. Cell condition data may beacquired in an automated fashion under microprocessor control. Cellcondition data may be acquired and stored in a format useable by anassociated data processing device. A graphical transformation of cellvoltage response data may be implemented to facilitate evaluation andanalysis of state of charge and overall cell condition.

Repetitive test signal summation and integration techniques may be usedto reduce the interference of ambient noise. Test signals of fixedfrequency may be provided, as may be test signals of differentfrequencies. A well-defined test signal may be used to ensure evaluationof the cell under test at a wide range of waveform periods. The voltageresponse of a cell under test may be created and captured in a form tofacilitate analytic evaluation of the cell using Fourier, Laplace andrelated techniques. Similarly, the voltage response of a cell under testmay be created or captured in a form to facilitate evaluation by neuralnetworks.

The technique permits rapid and accurate acquisition of informationrelevant to the state of charge and qualitative information about anelectrochemical energy storage device, commonly referred to as abattery. The technique may provide a precision test instrument thatproduces precise driving signals to create polarization responsevoltages as a function of time which are developed across anelectrochemical cell or battery of cells in response to a galvanic(current) stimulation, and may be captured to present data reflectingstate of charge and cell quality information. The technique includesspecific noise reduction and small signal detection and processingcapabilities to permit the use of non-invasive driving signals. Thetechnique further relates to acquiring and manipulating data tofacilitate analysis and presentation of detailed information rapidly andefficiently.

The invention features determining polarization voltages developed inresponse to an excitation signal applied to a device. Such polarizationvoltages may be determined by using a controlled-current sourceconfigured for connection to a first terminal of the device, acontrolled-voltage source configured for connection to a second terminalof the device, a sensor configured to sense a voltage across the deviceand to produce a sensor signal in response to the voltage, and acontroller connected to the controlled-current source, thecontrolled-voltage source and the sensor. The controller is configuredto determine polarization voltages in response to the sensor signal.

Embodiments of the invention may include one or more of the followingfeatures. The device may be an electrically-responsive element, network,electrochemical cell, or battery. The controlled-current source and thecontrolled-voltage source may be configured to provide self-centeringand autopolarity relative to the device. To this end, the controller maybe configured to provide self-centering relative to the device bysupplying a voltage equal to one half of the bias voltage of the deviceto the controlled-voltage source. The controlled-current source may beconfigured to provide a symmetric, bipolar square wave to the firstterminal of the device.

The controller may include a microprocessor and associated circuitry.Alternatively, the controller may be made up of analog circuitry.

Kelvin connection circuitry may be used to attach the components to thedevice. The Kelvin connection circuitry may include a first leadconnected to the controlled-current source and configured for connectionto the first terminal of the device, a second lead connected to thecontrolled-voltage source and configured for connection to the secondterminal of the device, and third and fourth leads connected to thesensor and configured to be connected to, respectively, the first andsecond terminals of the device.

A feedback loop may be employed between the sensor and the controller.The feedback loop may be configured to eliminate a nonvarying or slowlyvarying portion of the voltage across the device (e.g., the bias voltageof the device) so that the sensor signal reflects only a portion of thevoltage across the device.

In another general aspect, the invention features determiningpolarization voltages developed in response to an excitation signalapplied to a device by connecting a controlled-current source to a firstterminal of the device, connecting a controlled-voltage source to asecond terminal of the device, and using a controlled-current source toapply a bipolar, symmetric square wave to the device. A voltage issensed across the device to produce a sensor signal, and the sensorsignal is modified to eliminate effects of a nonvarying or slowlyvarying portion of the sensed voltage. Polarization voltages are thendetermined in response to the modified sensor signal.

The controlled-voltage source may be controlled to produce a voltagehaving a magnitude equal to one half of the bias voltage of the device.

A graphical representation of the polarization voltage suitable forimmediate visual inspection and analysis may be generated. Thepolarization voltage may be compared to baseline data for a class ofdevices to which the device belongs to assess a relative condition ofthe device.

Polarization voltage data obtained through testing with a symmetricbipolar square wave can manipulated in a fashion advantageous for aparticular form of graphic representation suitable for immediate visualinspection and analysis. The polarization voltage data also can be usedto assess the relative condition of an electrochemical cell or battery.Polarization response profiles are obtained for the device under testand compared to baseline data stored in memory. Specific differences inthe shapes of the response patterns are indicative of specific problemswithin the device under test and, for specific types of devices undertest, only certain data points, corresponding to specific polarizationfrequencies, need be evaluated to make the necessary determination.

A DC offsetting signal may be permitted to vary during the test period,such that polarization voltage data may be obtained through testing witha symmetric bipolar square wave concurrently with DC charging ordischarging current being supplied to the device under test.

Changes in the polarization voltage of a cell can be used to accuratelydetermine the end-of-charge point, which is reached when at least one ofthe chemical species needed for the recharge reaction has beeneffectively depleted, whereupon the equivalent Faradaic resistance(characteristic of the electrode-electrolyte interface) commences aprecipitous increase that is manifested as a commensurate increase inthe measured polarization voltage, and is especially apparent atrelatively low equivalent polarization frequencies in the range of 1 to0.01 Hertz. When such a rise is detected, it may be used as anindication of end-of-charge, and so employed as a stopping signal for aconcurrent charging excitation.

The waveforms produced may be arbitrary. That is, the waveforms may becomprised of sine waves, triangle waves, ramps, pulses, complexparametric shapes or any combination thereof, in order to assess thevarious time dependent characteristics of galvanically stimulated cellsand electrical networks.

The time dependent evolution of polarization voltages may be measuredaccording to various digital sampling time schedules, such as thosecharacterized as a constant ΔT schedule, wherein the time elapsedbetween successive samples is held constant; a logarithmic ΔT schedule,wherein the time elapsed between successive samples is increased in anexponential manner; or a parametric ΔT schedule, wherein the timeelapsed between successive samples is determined by a set of valuesprogrammed into the prestored software. Nonlinear sampling schedules,when properly constituted to accurately capture the polarization eventsof interest for a particular chemistry, confer the advantage of aconsiderable reduction in data collection and storage requirements. Inthe ultimate case, only a very few data points may be required, allowingthe entire method to be incorporated into a single, relatively simple,integrated circuit.

Other features and advantages of the invention will become apparent fromthe following description, including the drawings, and from the claims.

BRIEF DESCRIPTION OF THE DRAWING

FIGS. 1A-1D are block diagrams of a test device.

FIG. 2 is a block diagram illustrating a centering effect of the testdevice of FIGS. 1A and 1B.

FIGS. 3A and 3B are graphs, respectively, of a single frequency drivingsignal used to evaluate a cell under test and a nominal cell potential.

FIGS. 4A and 4B are graphs of a voltage response across a cell undertest.

FIGS. 5A and 5B are graphs of a voltage response across a cell undertest.

FIGS. 6A-6C are graphs of a half cycle of the voltage response across acell under test.

FIGS. 7A and 7B are graphs of a tester output signal.

FIG. 8 is a graph of a logarithmic map of a tester output signal.

FIGS. 9A and 9B are graphs of a tester output signal.

DESCRIPTION

Referring to FIG. 1A, a tester 10 develops a time varying polarizationvoltage across a device under test 12, and detects, measures andprocesses the polarization voltage. Device 12 has two electricalterminals, which are hereinafter designated as a positive terminal 16and a negative terminal 18. A current signal 14 is imposed across thedevice 12 by a current driver 22. Current driver 22 may includeconventional components. In one implementation, the current driver 22includes a voltage controlled current source. In general, current driver22 must be capable of producing a sustained bipolar current drive signal14 which takes the form of a precise square wave. Current driver 22 iselectrically connected to one terminal of device 12. The oppositeterminal of device 12 is similarly connected to a current receiver,which may include a voltage controlled voltage source. Current receiver24 exhibits negligible output impedance for the drive signal 14 providedby current driver 22 and transmitted through the device under test, andso serves as a virtual AC ground. A preamplifier 30 also is connectedacross the terminals of device 12. The preamplifier 30 senses, isolates,and amplifies the polarization voltage induced across the internalimpedance of device 12 by the current 14 supplied by driver 22. Systemcontrol, data processing and I/O functions are provided by amicroprocessor 40, such as an Intel 80386 processor, and associatedanalog and digital components.

Kelvin Connection & Signal Detection

Device 12 is connected to the tester 10 using four leads connected sothat each lead makes an individual connection directly to theappropriate terminal of the device 12. This connection method, known asa Kelvin connection, reduces the interaction between the drivingcircuitry (i.e., current driver 22, current receiver 24, and theirassociated connection leads) and the sensing circuitry (i.e.,preamplifier 30 and its associated connection leads). By virtue of thedirect connection of the preamplifier test leads to the terminals ofdevice 12, and the relatively high input impedance of preamplifier 30,no drive current flows through any part of the sensing circuitry, andthe detected polarization voltage is completely attributable to device12. Referring also to FIG. 1B, detection and analog processing of thepolarization response signal is provided by preamplifier 30, which mayinclude four operational amplifiers 54, 56, 58 and 64 to accomplishvoltage sensing, DC offset compensation, and amplification functions ofthe preamplifier 30. Terminals 16 and 18 of device 12 are electricallyconnected to respective positive and negative inputs of aninstrumentation amplifier 54, which may take the form of a differentialamplifier having a very high impedance, unity gain, and excellent commonmode rejection. A signal 55 produced by instrumentation amplifier 54 isequal to the potential difference between the inputs of the amplifier54. When device 12 is an electrochemical cell or battery having anintrinsic DC bias potential of its own, signal 55 will include this biaspotential to which is added a polarization voltage component that isdeveloped across the internal impedance of device 12 by the drivecurrent 14.

Because the signal of interest is only the relatively small polarizationvoltage component of the full measured device potential, it is useful toremove the effects of any DC bias component from the output ofpreamplifier 30. This is accomplished using an offset generator 50 thatsupplies a suitable DC offsetting voltage signal 52 to an invertingscaling amplifier 64. A summing amplifier 56 combines the invertedoffset voltage produced by the scaling amplifier 64 with the signal 55to produce a signal 57 corresponding to the polarization voltage. Thevalue of the offset voltage is determined by the microprocessor 40.

As noted, preamplifier 30 provides an output signal 55 equal to thetotal potential present between the terminals of device 12. This outputis conveyed to a low-pass filter 60 that is configured to remove higherfrequency components from the signal 55 to provide a filtered DC voltage61 to a multiplexer 62. The microprocessor 40 controls the multiplexer62 to route this signal to an A/D converter 64 that in turn conveys adigital representation of the signal 61 to microprocessor 40. Themicroprocessor then issues digital commands to offset voltage generator50, which may include a digitally-controlled voltage source. The offsetvoltage generator 50 responds by providing an offsetting voltage 52having a magnitude equal to one half of the DC potential present acrossdevice 12, and having the same relative polarity as terminal 18 ofdevice 12. The offsetting signal 52 is conveyed to the scaling amplifier64, which amplifies this signal by a factor of negative two to producean output 65 that equals the DC component of signal 55 in magnitude, butis of opposite polarity. As noted, the signals 55 and 65 are conveyed tosumming amplifier 56, which sums them to produce the signal 57. This, ineffect, subtracts the DC bias component 65 from the signal 55 to removethe DC component associated with any intrinsic DC potential present indevice 12 and isolate the polarization voltage component as signal 57.Signal 57 is thereafter provided to the input of a high gain amplifier58, which has an amplification factor of about 1500, to produce apolarization voltage output 32 that represents the signal of interest ina form conveniently used by digital and analog instruments.

Signal 32 is conveyed to a unity gain buffer 37 that provides anisolated output for test bed instrumentation, such as an oscilloscope orother visual display device. The buffer 37 prevents interaction betweenpreamplifier 30 and the analog instrumentation 38.

Digitization of Polarization Signal

Signal 32, representing the isolated and amplified polarization voltage,is supplied to an A/D converter 34 that converts the signal 32 into adigital signal 36 having a series of digital samples. The converter 34is controlled by microprocessor 40, which forwards a clock signal 42 tothe converter. Each digital sample represents the instantaneous value ofsignal 32 at a point in time corresponding to a clock pulse. The digitalsignal 36 is passed to microprocessor 40 for processing, storage andtransmission.

Auto Centering/Auto Polarity Function

Offset signal 52 is also used to provide a self centering effect. Signal52 constitutes the input signal to current receiver 24, and, as notedabove, is set by microprocessor 40 to have one half the magnitude of theDC bias voltage of device 12 and the same polarity. A primary attributeof the current receiver 24 is that its output voltage is maintained at alevel equal to its input voltage, irrespective of the output loadcurrent. This means that terminal 18 of device 12, which is connected tocurrent receiver 24, will be maintained at a voltage equal to one halfof the total DC bias of device 12, having a polarity equal in sign tothe actual polarity of terminal 18 of device 12, as determinedpreviously by the microprocessor 40.

Terminal 16 of device 12 is electrically connected to current driver 22,which is a voltage controlled current source exhibiting very high outputimpedance. As such, the output of current driver 22 will assume whatevervoltage potential, with respect to the relative potential of device 12,is required to ensure delivery of the proper output current as isfunctionally determined by a controlling input signal 21. Thus, byemploying both a virtual ground current receiver 24 that maintains acontrolled DC potential, along with a highly compliant current driver22, the DC bias voltage presented by the device 12 is, in effect,centered with respect to local signal ground, as shown in FIG. 2. Forexample, if device 12 has a DC bias voltage of six volts, the positiveterminal 16 of device 12, which is connected to current driver 22, willbe three volts above ground, while conversely, the negative terminal 18will be three volts below ground. This offers great advantages forportable implementations that operate using a battery pack power supply.By ensuring that the cell voltage will be centered about signal ground,the total battery pack voltage that is necessary to ensure properoperation of the electronic circuitry, is thereby minimized.Furthermore, this arrangement makes the relative polarity of theconnections between the test system and the terminals of the deviceunder test 12 irrelevant. Thus, if device 12 is attached to the systemwith its negative terminal 18 connected to current driver 22 and itspositive terminal 16 connected to current receiver 24, the control loopdescribed by preamplifier 30, low pass filter 60, multiplexer 62 A/Dconverter 64, and microprocessor 40, will produce an offset voltagesignal 52 of the same polarity as terminal 16 of device 12. That signalserves as the input to current receiver 24, which then presents thatvoltage and polarity back to device 12, properly matching the polarityof device 12 and again centering the DC bias voltage of device 12 aboutthe local signal ground.

Generation of Drive Signal

The control signal 21 for current driver 22 is provided by WaveformGenerator 48, under control of the microprocessor 40. The control signaltakes the form of a precise square wave voltage signal having severalimportant characteristics, as may be seen in FIG. 3. A primarycharacteristic of this signal is that is exhibits symmetry about thehorizontal (time) axis. As indicated in FIG. 3, a single cycle of signal14 may be subdivided into two distinct half-cycles of equal duration.The positive half-cycle from to to t₀ to t₂ and the negative half-periodfrom t₁ to t₂ must be of equal and constant duration for each full cycleof the waveform. To ensure accurate charge balancing over the course ofeach waveform cycle the duty cycle of each square wave must be 50%, andadditionally, the half-cycle timing variance (skew plus jitter) within awhole cycle should preferably not exceed 20 nanoseconds. Similarly, thesignal amplitude during a single cycle must be constant. By ensuringsymmetry both in the amplitude and time domains, the galvanic excitationprovided to Device 12 will have a net DC current value of zero whensummed over an integral number of cycles. The amplitude and thefrequency of signal 14 may take a number of different values, but toensure that the drive signal does not significantly alter the state ofcharge of device 12, the amplitude is advantageously set so that thepeak to peak value of the polarization voltage produced across device 12does not exceed several millivolts per individual cell, and furthermorethat precisely an integral number of cycles are generated at eachspecific frequency. To ensure detection of a very fast process orphenomenon within Device 12, it is necessary that the rise time of thesquare wave drive current exceed, by a substantial margin, that of theprocess to be detected; otherwise, the measured response will reflectonly the properties of the driving signal and circuitry, not the deviceunder test. Hence, it is preferred that the square wave rise time be onthe order of one microsecond, in order to ensure that an accurate andmeasurable polarization response is created.

To allow direct determination of the current output of current driver22, a current sensing resistor 23 is connected in series with the outputof current driver 22. The drive current passes through this resistor,developing a proportional voltage which is detected by differentialinput current sense amplifier 25, whose output 27 connects tomultiplexer 64, which is under the control of microprocessor 40. Atvarious times, the multiplexer may be switched to route the currentsense signal 27 into A/D converter 64, whereupon the digitally sampleddrive current information is conveyed to the microprocessor forprocessing and storage.

Microprocessor Functions

Microprocessor 40 is a stored program microprocessor commerciallyavailable such as the Intel 80386 processor. Microprocessor 40 providesoutputs to, and accepts inputs from, user interface 44 which includes akeypad and visual display microprocessor 40 is further provided with astandard serial interface 45 to permit data exchange between the systemand an external computer or other digital device. Microprocessor 40 isresponsible for overseeing and managing the operation of the overallsystem. Microprocessor 40 may also be provided with random access memory46 of conventional design, and sometimes other supporting devices aswell, to permit the storage and manipulation of user inputs, data andoutputs.

Circuit Variations

Variations on the circuit of FIG. 1B are provided in FIGS. 1C and 1D.FIG. 1C illustrates a variation in which the preamplifier 30 isimplemented using a four input instrumentation amplifier. FIG. 1Dillustrates an implementation in which the microprocessor is removedfrom the feedback loop.

In the implementation of FIG. 1C, the DC offset voltage generator 50develops two voltage signal outputs 52, 53 in response to an analoginput control signal. These outputs are each equal in magnitude to onehalf of the magnitude represented by the input control signal, but areof opposite polarity (e.g., V_(out1)=(+V_(in)/2); V_(out2)=(−V_(in)/2)).The preamplifier 30 of the circuit includes four voltage input terminalsand one output terminal, the first two inputs (designated A and B) areof the non-inverting sense with respect to the output signal, and thesecond two inputs (designated C and D) are of the inverting sense withrespect to the output signal. The output signal is a voltage thatincludes a highly amplified copy of the algebraic sum of the four inputvoltage signals (i.e., V_(out)=k(A+B−C−D)).

The microprocessor 40 may commence a preprogrammed sequence ofoperation, either as a result of a user input command, or (in the caseof an automatic instrument embodiment) as a result of detecting a changein the voltage present across the two preamplifier input circuits. Sucha voltage change signals the completion of a suitable connection to anexternal device under test.

The preprogrammed sequence may have an initial function of providing aproper control signal to a DC offset generator so as to null out theeffect on the preamplifier of the bias voltage present across theterminals of the device under test, and to center the bias potentialexhibited by the device under test about local analog ground. This maybe achieved as follows. First, the controller receives a sense signal,via the analog-to-digital converter 34, that is representative of thevoltage output of the preamplifier and is of the same polarity, butsubstantially amplified in magnitude, as the potential present acrossthe externally connected preamplifier input circuits, due to theintrinsic bias of the device under test. Next, in response to this sensesignal, the controller, via a digital-to analog converter (“DAC”) 49,commences outputting a constantly increasing control signal to the DCoffset generator. The control signal has the same relative polarity asthe output of the preamplifier, and continues to increase in magnitudeas long as the output of the preamplifier is other than zero. In effect,this represents the behavior of an ideal non-inverting integrator. Theoutput of the DAC is conveyed to the input of the DC offset voltagegenerator. The DC offset voltage generator is provided with two outputshaving absolute magnitudes that are always the same and equal to onehalf of the magnitude of the controlling signal, but are possessed ofopposite relative polarity. The negative output, of opposite polarity tothe generator input, provides the controlling input to the currentreceiver. Both outputs are connected to the preamplifier, such that thepositive output is connected to preamplifier input D which has aninverting sense, and the negative output, of opposite polarity to thegenerator input, is connected to preamplifier input C which has anon-inverting sense. Thus, provided the voltages presented by the DCoffset generator will algebraically cancel the voltage presented by thedevice under test, the DC potential of the preamplifier output will bezero.

If for example, the device under test is connected so that its positiveterminal is connected to both the current driver and the positive inputof the preamplifier input, and conversely, its negative terminal isconnected to the current receiver and the negative input of thepreamplifier, the output voltage of the current receiver will be seen tobecome increasingly negative with the passage of time, forcing thedevice under test's negative terminal, which was initially at ground, toassume an increasingly negative value. Note that the positive terminalof the device under test is connected to two high impedance nodes (e.g.,a high impedance input and a high impedance current source). As such,though the intrinsic bias potential of the device under test remainsconstant, the relative potential of the positive terminal will appear tobecome increasingly negative.

The output of the DAC will continue to slew until the voltage presentedat the output of the current receiver, as provided by the DC offsetgenerator, is equal in magnitude to one half of the intrinsic biaspotential of the device under test, and of the proper polarity such thatthe algebraic sum of the four preamplifier inputs will be preciselyzero, leading to a preamplifier output of zero. At that point, the inputto the non-inverting integrator, which in this case is simulated by amicroprocessor, is zero. This causes the slewing of the output of theDAC to cease.

The net effect of this differential integrator servo control loop istwofold. First, regardless of the actual connection of the test leads(i.e., it does not matter whether the current driver is connected to thepositive terminal of the device under test or not, and likewise for allthree other test leads, respectively), the loop action will cause thebias potential of the device under test to be precisely centered aboutlocal analog ground. Second, the DC bias of the device under test withrespect to the preamplifier is effectively nulled out, allowing verysmall polarization signals present differential across the terminals ofthe device under test to be highly amplified by the preamplifier andstill appear centered within its effective output dynamic range.

This technique has the further benefit of allowing a substantialdecrease in the required power supply voltages (with the attendantdecrease in cost, and in the case of portable embodiments, a substantialdecrease in size and weight) which are required to accommodate a deviceunder test of given bias potential, as compared to traditional DCcoupled methods wherein one terminal of the device under test remainsfixed at relative ground, and the other terminal may appear either aboveor below ground by an amount equal to the relative bias voltage,depending on the polarity of the test lead connections. Of course, theproblem of polarity could be simply avoided by employing capacitivecoupling techniques, but this severely affects the accuracy of anymeasurement at low frequencies, and renders measurement impossible forDC excitation signals.

The offset generator may be configured to provide either a either afixed DC offsetting signal or a tracking DC offsetting signal. Thesignals output by the offset generator may then either be held at afixed value until the termination of the present testing sequence(representing fixed DC bias offsetting), or may vary under control ofthe microprocessor (via the virtual integrator function) during theduration of the testing period representing tracking DC bias offsettingto compensate for changes in the bias voltage of the device under testcaused by charging or discharging currents from some external source, oras a result of any other variation in the bias potential of the deviceunder test. Suitable algorithmic corrections can be applied to thepolarization voltage data to compensate for the distortions created inthe case of the tracking (integrator) operation.

In the implementation of FIG. 1D, resistors 81 and 82 are optional, andmay be installed to provide bias current to buffers 83 and 84. Buffers83 and 84 are unity gain amplifiers that exhibit high input impedance soas not to load, or draw current from, the device 12. Resistors 85-88 mayhave values of about 2000 ohms, with values matched to within 0.01percent to provide adequate common mode rejection. Amplifier 90 is ofthe high gain instrumentation type, having high impedance inputs.Amplifiers 93 and 96 constitute, with their associated componentryparticularly with respect to resistors 94 and 95, which are very wellmatched so that amplifier 96 behaves as a highly accurate unity gaininverter, a differential output integrator, having the knowncharacteristic that its outputs will remain constant provided its inputis zero. The differential integrator outputs are connected to resistors87 and 88, in a manner that the integrator outputs will automaticallyadjust to force the net DC value of the preamplifier output to alwaysmaintain a zero value. The time constant of the integrator is set by theproduct of resistor 91 and capacitor 92, and must be adjusted so thatthe lowest input frequencies of interest are not substantiallyattenuated. In an alternate configuration, this time constant may bemade adjustable under external control, as, for example, by the use of adigitally controlled resistance element in place of resistor 91.

Operational Description of the Technique & Analysis Algorithms

Polarization voltage signal 32, shown schematically in FIGS. 3 and 4,represents the voltage response developed across the device under testby the drive current. Because the drive current signal is symmetric andperiodic, and of sufficiently small amplitude to ensure linear responsein device 12, the resultant polarization voltage will exhibit similarsymmetries. In most cases of interest, particularly for electrochemicalaccumulators, the polarization response exhibits several recurringcharacteristics. At time t₀, corresponding to the abrupt positivetransition of the drive current, the polarization response undergoes asimilarly rapid change. Due to the very short rise time of the squarewave drive current, this stepwise change of the response represents thetime-invariant part of the polarization, and is therefore attributableto the ohmic (real) component of the device's impedance. As can be seenin the figures, there may also be a small overshoot, due to the combinedinductive characteristics of device 12 and the test fixturing itself.Proper attention to fixturing will reduce stray inductances tonegligible levels and allow the device's own inductive response (whichtypically lasts from one to several hundred microseconds) topredominate.

Immediately following the decay of any inductive overshoot and for theremainder of the half cycle, the response is seen to increasemonotonically in magnitude in a non-linear fashion (unless the deviceappears purely resistive leading to a simple flat topped square waveresponse). In particular, the slope (first derivative) of this curvedresponse is seen to progressively decrease throughout each half-period,and is recognizable as being similar to the well known exponentialfunction (1-e^(1/t)), which is used to describe electrical circuitscontaining resistive and capacitive elements. This curved portion ishereinafter considered the time-varying component of the polarizationresponse, and is often composed of at least two distinct portions,arising from processes having different underlying time constants. Theseare identified in FIG. 4B as the fast (74) and slow (75) processes,respectively, and exhibit commensurately differing curvature. Fastprocesses tend to expend themselves in the early part of eachhalf-cycle, while the later tail section takes its shape from slowprocess and so changes relatively gradually over time.

At t₁, the next stepwise current transition occurs, whereupon apolarization curve of similar shape appears, but now tending downward.Provided that neither the condition nor state of charge of device 12changes appreciably during several consecutive excitation periods(square wave cycles), it is apparent that the shape and size of overallresponse waveform will remain relatively constant as well. In general,the polarization voltage signal 32 is well behaved and, except for adiscontinuity at each stepwise edge transition, is continuous.

The polarization response is digitized by converter 34, according to asampling schedule controlled by the microprocessor 40. To accuratelycapture the all the details of an arbitrary waveform, digital samplingtheory teaches that the sampling rate must be at least twice as high asthe highest frequency component of interest to avoid aliasing errors,and in practice, ten-times oversampling is used to ensure the fidelityof the digitized waveform.

Conventional digitization techniques employ a fixed interval (e.g., ΔT=aconstant) sampling schedule, wherein the analog wave form is repeatedlysampled and digitized, synchronously with a sample clock control signalhaving a constant frequency (f=1/ΔT). As is well known to practitionersof the art, constant ΔT sampling is required if the data is to beanalyzed using discrete transforms (Laplace or Fourier). The attainableresolution of such transform analyses is limited by the magnitude of ΔT,in that decreasing ΔT (that is, increasing the sampling rate) allowsfaster processes, or equivalently, higher component frequencies, to beresolved. Since typical electrochemical cells often exhibit transientresponses in the microsecond range, particularly when galvanicallyexcited by a square wave, it would appear that a very high sampling rateis preferred. Furthermore, when testing electrochemical accumulatorswhose behavior is governed in part by relatively slow kinetic processessuch as diffusion, a very low frequency square wave excitation (0.1 and0.01 Hertz) is required to elicit a significant polarization response.

When such a slow waveform is repetitively sampled at a high rate, a verysubstantial number of digitized values will be accumulated, especiallyif the test procedure includes many cycles of the waveform to. ensureadequate noise averaging. For many applications, particularly low costcommercial or portable device embodiments, the burden of raw datastorage and management presented by such a large data set isprohibitive.

Although constant ΔT sampling of a device's response may be desirableand necessary for certain analytical transform methods, a valuableaspect of the present invention is a novel non-linear sampling methodwherein ΔT is progressively increased within each half cycle.

Fast processes run to completion within the first few tens ofmilliseconds of each half-cycle. To capture the details characterizingthese early, rapidly evolving events, fast sampling is surely necessary.

Conversely, there are other slower processes which evolve over a timescale of many seconds. These are manifest in the tail section with itsmuch gentler slope and commensurately diminished high frequency content,thus allowing a substantially relaxed sampling schedule to be employed.

Therefore, when the actual time domain response of the evolvingpolarization voltage is of interest, a non-linear sampling schedule isprescribed whereby the inter-sample time is progressively increased in aparticular fashion throughout each half-cycle. Excellent resolution isachieved for both the early, fast as well as for the later slowerpolarization processes, with a total accumulation of far fewer actualdata points as compared to the conventional constant ΔT samplingparadigm.

The preferred non-linear sampling sequence is based on a geometricallyincreasing series of inter-sample delay times δt_(i), each of whichrepresents an integral number of base clock periods ΔT_(B) derived froma separate fixed frequency oscillator, preferably operating at onemegahertz or higher. The general algorithm for generating an appropriateseries of sample events is based on an exponential relationship:

δt _(i) =[ΔT _(B) ]×[K _((a×i)],) i=0, 1, 2, . . . , N

where δt₁ represents the time delay of the ith sample with respect tothe preceding step transition, ΔT_(B) is the period of the base clock(typically 1 microsecond), and K and a are appropriately selectedconstants. Note that when the index i increments uniformly as shownabove, the ratio of adjacent time delay values will be a constant valueequal to [ΔT_(B)]×[K^((a))]. If K is set to 2 and a is 1, then as iranges from zero to some limit N, a simple binary series of time delaysis generated, e.g., {1 ms (delay of first sample from step), 2 ms, 4 ms,8 ms . . . }. Moreover, in some cases, it may be preferred to omit thefirst few samples in each series, particularly to avoid the peak causedby the inductive behavior of the device 12. By appropriate selection ofthe three constants, a series can be constructed which provides manyclosely spaced samples during the early part of the polarizationwaveform where fast events occur, with fewer samples later on as therate of change of the polarization voltage is diminishing. By resettingi to zero at each stepwise transition and then incrementing to N, anidentical sampling schedule is generated for each half-period, greatlysimplifying later analysis. FIG. 5A shows a typical polarizationwaveform, with seven exponentially spaced sampled data points {S_(i),i=0 to 6} in each half-cycle.

1. First Transformation Step: Graphic Normalization & Averaging

Once the sampled data is collected, a normalization transformation isperformed, whereby the time varying portion of the response is separatedfrom the step-wise transition. This transformation may be applied toeither uniformly or nonlinearly sampled data. Referring to FIG. 5, thepolarization voltage value of S₀ (at time T₀), being the first samplefollowing the transition, is used as a reference value, and isnormalized by convention to a value of zero, as shown in FIG. 5B. Theactual voltage difference between sample S₀ and S₁ is then calculatedfrom the raw data and used as the y-value for S₁ in FIG. 5B; successivesamples are treated similarly, leading to an upward tending curve thatintersects the x-axis at time T₀. The magnitude of the difference,designated ΔE₀, between sample S₀ and the final sample from thepreceding half-period represents the size of the step. In FIG. 5B, themagnitude E of the step is plotted immediately to the left of samplepoint S_(0′), at time T₆. In the graph, a line is shown connectingpoints S₆ and S₀. In fact, the transition of the polarization voltagebetween these points is very rapid, and so that point S₆, if plottedaccording to the time scale used for all the other sample points, wouldappear almost directly above point S₀. To facilitate interpretation ofthe graphic data in FIG. 5B, point S₆ has been shifted slightly to theleft and a connecting line drawn to point S₀.

This transformation is applied individually to the data from eachhalf-cycle, resulting in a set of vectors each containing N+2 elements(that is, samples S₀ to S_(N), plus the ΔE₀ value). To ensure that thedata contains no artifacts, the information from the first twohalf-periods (one complete square wave cycle) may be omitted fromsubsequent analyses. The remaining M vectors are then divided into twogroups (corresponding to positive and negative half-cycles, according tothe sign of the excitation current) as shown in FIG. 3A. Each of thesegroups can be formally described as a two-dimensional matrix, comprisedof M vectors, corresponding to the number of whole cycles used in theanalysis, containing N+2 elements. Within each matrix, the values ofcorresponding elements are added together and these sums are eachdivided by the number of vectors in the matrix, yielding a single N+2element vector representing the mean value of all the vectors in thematrix; these are designated as the mean positive vector and the meannegative vector.

As is well known to practitioners of the art, such an averagingtechnique when applied across M cycles of a periodic waveform, serves toreduce the effect of any random noise signals present within the rawwaveform data, by approximately a factor of M^((0.5)).

Provided that device 12 is in an open-circuit state, and the internalchemical reactions behave reversibly for the small excitation signalsemployed (and do not exhibit any hysteresis effects), the shapes of themean positive and mean negative vectors will be mirror images, reflectedacross the x-axis, specifically, when all the element values in the meannegative vector are multiplied by minus one (hence, are normalized bysign inversion), the resultant inverted negative mean vector shouldperfectly match the mean positive vector. Any difference between thesetwo sign-normalized vectors indicates either that state of theelectrochemical system within device 12 changed during the dataacquisition period, or that device 12 was behaving in a nonlinearfashion as a result of the excitation itself. Provided that these meanvectors are congruent, they may be averaged, yielding a single vectorcharacteristic of the device under test. A graphic presentation of thesevectors is immediately useful for qualitative understanding of thedevice's performance and condition.

2. Second/Third Transformation Step: Linear to Log Time Axis

In the preferred embodiment, to further aid comprehension andunderstanding of the mean vector data, two additional transformationsare undertaken. These require either that the data has been sampledaccording to an exponentially derived schedule, or that evenly sampleddata has been resampled (decimated) according to a similar exponentialrule. In FIG. 6A, a typical positive-going mean vector is shown as acontinuous curve, with the actual sampled data points indicated. Theaccompanying legend provides the correspondence between each samplepoint (either identified by an integer index or as ΔE₀) and its relativetime of acquisition, in base clock periods, relative to the step-wisetransition. The index values increment uniformly, while the time valuesincrease exponentially.

When the data is replotted using the integer index values as the xcoordinate, FIG. 6B results, now exhibiting a well-known logarithmiccharacteristic, due to the fact that the index of each point is directlyproportional to the logarithm of its associated time value, δt₁. Notethat each point in linear space finds correspondence with a unique pointin logarithmic space. This transformation facilitates immediate visualidentification of curvature changes which signal the occurrence ofunderlying processes. Details of fast processes are sufficiently spreadout to be readily apparent, while the portion of the graph allotted toslower processes is relatively compressed without loss of any importantinformation.

A further manipulation of the logarithmically transformed data isperformed, by simply reflecting the curve about the vertical axis, asshown in FIG. 6C, and translating it horizontally so that the data pointS₀, corresponding to the last element in the mean vector, becomes they-intercept. These point are re-labeled in the graph, for reasons whichnow become apparent.

In the preferred embodiment, the information of interest relates to thechange of polarization voltage as it evolves during each half-cycle ofthe excitation current. Each sampled data point is uniquely identifiedby an offset interval δt_(i), measured with respect to the previoustransition. It is useful to define a new quantity, the equivalentpolarization frequency F_(Pi), referred to hereinafter as thepolarization frequency, which is equal to 1/(2×δt_(i)). In this manner,the point associated with the lowest measured polarization frequency(that is, having the longest interval since the prior transition)appears leftmost on the graph, with ascending frequencies proceeding tothe right. The graph is again logarithmically scaled with respect topolarization frequency, such that while the ratio of adjacentfrequencies is constant, succeeding points are uniformly spaced alongthe x-axis. This manner of presentation, plotting polarization frequencyalong the abscissa, has been found to be more convenient and more easilyunderstood by those familiar with the art. Viewing polarization responsein terms of frequency allows immediate comparison to the vast amount ofFrequency Response data available in the “Impedance Spectroscopy”literature.

The present invention supports qualitative and quantitative analysis ofenergy cells. FIG. 7A provides a typical polarization response of afully charged lead-acid cell. The peak to peak magnitude of the responseacross the cell is preferably not greater than several millivolts, topreserve linear response. FIG. 7B is the response of the same cell, in adischarged condition. Intermediate states of charge exhibit curvesfalling between these two extremes. At progressively higher chargestates, the magnitude of ΔE₀ decreases monotonically, while thesteepness, and hence the overall height of the waveform, increases. Thetwelve curves presented in FIG. 8 represent data from a single 12 voltlead-acid automotive battery at different states of charge. The boldline represents the mean values of the sample population at full charge,while the others depict the response of the battery discharged and atten ascending states of charge. This sequence reflects the changesproduced by ten one hour charge events, each at the C/10 rate. For afully charged battery, the curve appears steeply curved, with thepolarization voltage increasing as the polarization frequency decreases.In the discharged state, the curve is nearly horizontal, exhibiting atthe high frequency (right) end, a value approximately twice that of thecharged unit. Intermediate charge values fall between these two curves.

Predictable real-time variations in the peak-to-peak amplitude of thepolarization response can be used to detect the end of charge conditionin a lead-acid battery. A constant frequency square wave excitation (at0.1 Hz) is preferred, and the response is continuously monitoredthroughout the charging process. Under dynamic conditions (charging ordischarging), the offsetting voltage is continually adjusted tocompensate for the changing potential of the device under test. As thebattery approaches its fully charged state, the amplitude envelope(peak-to-peak value of polarization response) exhibits a rapidlyincreasing magnitude, indicating an increase in the Faradaic resistancefollowed by the onset of the oxygen evolution reaction as thepolarization voltage reaches the gassing point. The response curve of ahealthy cell will appear smoothly curved, with a steeply sloped onset,gradually tapering off to an asymptotic response (whose maximumamplitude is proportional to charging current). In contrast, anunhealthy cell that has a reduced level of absorbed electrolyte, due forexample to previous episodes of overcharging, shown a pronounced kneelin the curve: the rate of change of the polarization response (itsslope) abruptly assumes a lower value.

Two important factors are evident here, shown in FIGS. 9A and 9B. First,when the polarization response begins its precipitous rise, the cell hasaccepted all the energy it can for recharging so the energy is now goinginto electrolysis. At this point, it is preferable to discontinuecharging, since further energy input is no longer increasing thestate-of-charge, but is merely generating gas and unnecessary heat.Second, the knee in the curve is indicative of a relative increase inthe electrochemical depolarization process occurring at the negativeplate, due to the increase availability of gaseous oxygen which hasescaped from the electrolyte and is diffusing directly to the negativeplate. Thus, the presence of such a knee is symptomatic of cell dry out,that is, a depletion of electrolyte, as is often caused by excessiveovercharge.

What is claimed is:
 1. A system for determining the polarizationvoltages developed in response to an excitation signal applied to adevice, the system comprising: a controlled-current source configuredfor connection to a first terminal of the device; a controlled-voltagesource configured for connection to a second terminal of the device,wherein the controlled-voltage source is configured to provideself-centering and auto-polarity for the system; a sensor configured, tosense a voltage across the device and to produce a sensor signal inresponse to the voltage sensed across the device, and a controllerconnected to the controlled-current source, the controlled-voltagesource, and the sensor, the controller being configured to determinepolarization voltages in response to the sensor signal.
 2. The system ofclaim 1, wherein the controller comprises a microprocessor andassociated circuitry.
 3. The system of claim 1, wherein the controllercomprises analog circuitry.
 4. The system of claim 1, further comprisingKelvin connection circuitry, the Kelvin connection circuitry comprising:a first lead connected to the controlled-current source and configuredfor connection to the first terminal of the device, a second leadconnected to the controlled-voltage source and configured for connectionto the second terminal of the device, and third and fourth leadsconnected to the sensor and configured to be connected to, respectively,the first and second terminals of the device.
 5. The system of claim 1,wherein the controlled-current source is configured to provide asymmetric, bipolar square wave to the first terminal of the device. 6.The system of claim 1, further comprising a feedback loop between thesensor and the controller, the feedback loop being configured toeliminate a portion of the voltage across the device corresponding to abias voltage of the device so that the sensor signal reflects only aportion of the voltage across the device.
 7. The system of claim 6,wherein the controller is configured to provide self-centering relativeto the device by supplying a voltage equal to one half of the DC offsetvoltage to the controlled-voltage source.
 8. A method of determiningpolarization voltages developed in response to an excitation signalapplied to a device, the method comprising: connecting acontrolled-current source to a first terminal of the device; connectinga controlled-voltage source to a second terminal of the device, whereinthe controlled-voltage source is controlled to produce a voltage havinga magnitude equal to one half of the non-varying portion of the sensedvoltage; using a controlled-current source to apply a bipolar, symmetricsquare wave or other waveforms to the device; sensing a voltage acrossthe device to produce a sensor signal in response to the voltage sensedacross the device, and; modifying the sensor signal to eliminate effectsof a bias voltage of the device; and determining polarization voltagesin response to the sensor signal.
 9. The method of claim 8, furthercomprising generating a graphical representation of the polarizationvoltage suitable for immediate visual inspection and analysis.
 10. Themethod of claim 8, further comprising comparing the polarization voltageto baseline data for a class of devices to which the device belongs toassess a relative condition of the device.